Integrand size = 13, antiderivative size = 13 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2 \sqrt {1+x^3}}{3} \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267} \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2 \sqrt {x^3+1}}{3} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {2 \sqrt {1+x^3}}{3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2 \sqrt {1+x^3}}{3} \]
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Time = 1.94 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
default | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
trager | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
risch | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
elliptic | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
pseudoelliptic | \(\frac {2 \sqrt {x^{3}+1}}{3}\) | \(10\) |
gosper | \(\frac {2 \left (1+x \right ) \left (x^{2}-x +1\right )}{3 \sqrt {x^{3}+1}}\) | \(21\) |
meijerg | \(\frac {-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {x^{3}+1}}{3 \sqrt {\pi }}\) | \(24\) |
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none
Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2}{3} \, \sqrt {x^{3} + 1} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2 \sqrt {x^{3} + 1}}{3} \]
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none
Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2}{3} \, \sqrt {x^{3} + 1} \]
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2}{3} \, \sqrt {x^{3} + 1} \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^2}{\sqrt {1+x^3}} \, dx=\frac {2\,\sqrt {x^3+1}}{3} \]
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